SOLUTION: a car and a train leave station A at the same time for station B, 220 miles away. if the speed of the car averages twice the speed of the train and the car arrives 5.5 hours before

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: a car and a train leave station A at the same time for station B, 220 miles away. if the speed of the car averages twice the speed of the train and the car arrives 5.5 hours before      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 621342: a car and a train leave station A at the same time for station B, 220 miles away. if the speed of the car averages twice the speed of the train and the car arrives 5.5 hours before the train, find the speed of the car and the speed of the train.
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the speed of the car
Let +b+ = the speed of the train
Let +t+ = the time it takes for the
train to get to station B.
--------------------
Equation for the train:
(1) +220+=+b%2At+
Equation for the car:
(2) +220+=+a%2A%28+t+-+5.5+%29+
(3) +a+=+2b+
-------------
Substitute (3) into (2)
(2) +220+=+2b%2A%28+t+-+5.5+%29+
and, from (1),
(1) +t+=+220%2Fb+
Substitute this into (2)
(2) +220+=+2b%2A%28+220%2Fb+-+5.5+%29+
(2) +220+=+440+-+11b+
(2) +11b+=+220+
(2) +b+=+20+
and, since
(3) +a+=+2b+
(3) +a+=+40+
The speed of the car is 40 mi/hr
The speed of the train is 20 mi/hr
check:
(1) +220+=+20t+
(1) +t+=+11+
and
(2) +220+=+40%2A%28+t+-+5.5+%29+
(2) +22%2F4+=+t+-+5.5+
(2) +22+=+4t+-+22+
(2) +4t+=+44+
(2) +t+=+11+
OK

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a car and a train leave station A at the same time for station B, 220 miles away.
if the speed of the car averages twice the speed of the train and the car arrives 5.5 hours before the train, find the speed of the car and the speed of the train.
:
Let s = speed of the train
then
2s = speed of the car
:
Write a time equation, time = dist/speed
:
Train time - car time = 5.5 hrs
220%2Fs - 220%2F%282s%29 = 5.5
Reduce the 2nd fraction
220%2Fs - 110%2F%28s%29 = 5.5
Subtract like terms
110%2Fs = 5.5
110 = 5.5s
s = 110%2F5.5
s = 20 mph is the speed of the train
You can find the speed of the car, check solutions by finding the time of each